Probability • Topic 2 of 3

Simple Events and Likelihood of Events

What is a Simple Event?

A simple event is an event that has only one outcome. For example, rolling a 3 on a die is a simple event. Drawing a king of hearts from a deck is a simple event.

What is an Event?

An event can be a single outcome or a set of outcomes. Events can be categorized by their likelihood.

Types of Events by Likelihood:

Likelihood	Description	Probability	Example
Impossible	Cannot happen	0	Rolling a 7 on a standard die
Unlikely	Small chance of happening	Between 0 and 0.5	Drawing an ace (4/52 ≈ 0.077)
Even Chance	Equally likely to happen or not	0.5	Getting heads on a coin flip
Likely	Good chance of happening	Between 0.5 and 1	Drawing a non-ace (48/52 ≈ 0.923)
Certain	Will definitely happen	1	The sun will rise tomorrow

Complement of an Event:

The complement of an event A (written as $A'$ or $\bar{A}$) includes all outcomes NOT in A.

$P(A) + P(A') = 1$ or $P(A') = 1 - P(A)$

Example: If P(rain) = 0.3, then P(no rain) = 1 - 0.3 = 0.7

Probability Rules:

All probabilities are between 0 and 1 inclusive: $0 \leq P(A) \leq 1$
Sum of probabilities of all possible outcomes = 1
$P(\text{impossible event}) = 0$
$P(\text{certain event}) = 1$

Likelihood Scale with Examples:

Event	Probability	Likelihood
Winning lottery with one ticket	~0.0000001	Very unlikely
Getting an even number on die roll	0.5	Even chance
Getting at least one head in 2 coin flips	0.75	Likely

Solved Examples

Worked Example

A bag contains tickets numbered 1 to 20. A ticket is drawn at random. Find the probability that the number drawn is:

(i) even

(ii) odd

(iii) a prime number

(iv) greater than 15

Solution

Step 1: Total possible outcomes = 20
Step 2: (i) Even numbers: 2,4,6,8,10,12,14,16,18,20 → 10 numbers
P(even) = $\frac{10}{20} = \frac{1}{2} = 0.5$
Step 3: (ii) Odd numbers: 1,3,5,7,9,11,13,15,17,19 → 10 numbers
P(odd) = $\frac{10}{20} = \frac{1}{2} = 0.5$
Step 4: (iii) Prime numbers: 2,3,5,7,11,13,17,19 → 8 numbers
P(prime) = $\frac{8}{20} = \frac{2}{5} = 0.4$
Step 5: (iv) Numbers greater than 15: 16,17,18,19,20 → 5 numbers
P(>15) = $\frac{5}{20} = \frac{1}{4} = 0.25$

Answer: (i) 0.5, (ii) 0.5, (iii) 0.4, (iv) 0.25

Worked Example

The probability of raining tomorrow is 0.35. What is the probability that it will NOT rain tomorrow? Express as a percentage.

Solution

Step 1: Use complement rule: P(not rain) = 1 - P(rain)
Step 2: P(not rain) = 1 - 0.35 = 0.65
Step 3: Convert to percentage: 0.65 × 100% = 65%

Answer: P(not rain) = 0.65 or 65%

Worked Example

A spinner has 8 equal sections: 3 red, 2 blue, 2 green, 1 yellow. Classify the likelihood of each color using the terms: impossible, unlikely, even chance, likely, certain.

Solution

Step 1: Total sections = 8
Step 2: P(red) = $\frac{3}{8} = 0.375$ → Unlikely (between 0.1 and 0.4)
Step 3: P(blue) = $\frac{2}{8} = 0.25$ → Unlikely
Step 4: P(green) = $\frac{2}{8} = 0.25$ → Unlikely
Step 5: P(yellow) = $\frac{1}{8} = 0.125$ → Very unlikely (or just unlikely)
Step 6: Check sum: $0.375 + 0.25 + 0.25 + 0.125 = 1$ ✓

Answer: Red (unlikely), Blue (unlikely), Green (unlikely), Yellow (very unlikely)

Key Points

Simple event: Single outcome (e.g., rolling a 4)
Complement: All outcomes NOT in the event; $P(A') = 1 - P(A)$
Probability range: 0 (impossible) to 1 (certain)
Likelihood terms: Impossible, unlikely, even chance, likely, certain
Sum of probabilities of all possible outcomes = 1
The more likely an event, the closer its probability is to 1

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The probability of an event lies between:

Explanation: $0\le P\le1$.

Q2.An event certain to happen has probability:

Explanation: $1$.

Q3.An impossible event has probability:

Explanation: $0$.

Q4.$P(\text{a }3$ on a die$)=$

Explanation: $\tfrac16$.

Practice more MCQs → 📝 Assignment · 35 marks